Abstract. Reverse-time migration (RTM) of teleseismic converted and free-surface reflected phases has been successful in helping to constrain the structure of the crust and upper mantle, but its accuracy is to a large extent determined by the background velocity model used in the underlying wave propagation. To this end, we develop a technique for RTM based wave-equation reflection tomography i...

Let H0 be an arbitrary self-adjoint n × n matrix and H(n) be an n × n (random) Wigner matrix. We show that t 7→ Tr exp(H(n)−itH0) is positive definite in the average. This partially answers a long-standing conjecture. On the basis of asymptotic freeness our result implies that t 7→ τ(exp(a − itb)) is positive definite whenever the noncommutative random variables a and b are in free relation, wi...

Abstract. A spectral method for identifying lumping in large Markov chains is presented. Identification of meta stable states is treated as a special case. The method is based on spectral analysis of a self-adjoint matrix that is a function of the original transition matrix. It is demonstrated that the technique is more robust than existing methods when applied to noisy non-reversible Markov ch...

The main theorems below are Theorem 9 and Theorem 11. As far as I know, Theorem 9 represents a slight improvement over what currently appears in the literature, and gives a fairly easy proof of Theorem 11 which is due to R. Howe and C. Moore [4]. In the semisimple case, the Howe-Moore result follows from [6] or [7]. The proofs appearing here are relatively elementary and some readers will recog...

Kaltofen has proposed a new approach in Kaltofen (1992) for computing matrix determinants without divisions. The algorithm is based on a baby steps/giant steps construction of Krylov subspaces, and computes the determinant as the constant term of the characteristic polynomial. For matrices over an abstract ring, by the results of Baur and Strassen (1983), the determinant algorithm, actually a s...

Abstract Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution of large self-adjoint random matrices from the generalized unitary ensembles. This paper considers discrete Tracy–Widom operators, and gives sufficient conditions for a discrete integrable operator to be the square of a Hankel matrix. Examples include the discrete Bessel kerne...

We summarize the field-theory/matrix model correspondence for a chiral N = 1 model with matter in the adjoint, antisymmetric and conjugate symmetric representations as well as eight fundamentals to cancel the chiral anomaly. The associated holomorphic matrix model is consistent only for two fundamental fields, which requires a modification of the original Dijkgraaf-Vafa conjecture. The modified...

The subject of this article is the duality principle, which, well beyond its stand at the heart of Gabor analysis, is a universal principle in frame theory that gives insight into many phenomena. Its fiber matrix formulation for Gabor systems is the driving principle behind seemingly different results. We show how the classical duality identities, operator representations and constructions for ...

In 1961 Youla published his paper 'On the factorization of rational matrices'. He proved that any proper rational parahermitian matrix, positive definite on the imaginary axis can be factorized as the product of a proper rational matrix, stable with respect to the closed right half plane, and its adjoint. In this paper I prove that for any positive definite, nonstrictly proper matrix this facto...

In this paper, we give a proof of the equivalence of N = 1 SO/Sp gauge theories deformed from N = 2 by the superpotential of adjoint field Φ and the dual type IIB supersting theory on CY threefold geometries with fluxes and orientifold action after geometric transition. Furthermore, by relating the geometric picture to the matrix model, we show the equivalence among the field theory and the cor...